Simple Machines
Inclined Plane, Wedge, and Screw
Principles of Engineering
© 2012 Project Lead The Way, Inc.
The Six Simple Machines
Inclined Plane
Wedge
Screw
Mechanical Advantage (MA)
• Ratio of the magnitude of the
resistance and effort forces
• Ratio of distance traveled by the
effort and the resistance force
Calculated ratios allow designers to
manipulate speed, distance, force, and
function
Mechanical Advantage Example
A mechanical advantage of 4:1 tells us
what about a mechanism?
Magnitude of Force
Effort force magnitude is 4 times less than the
magnitude of the resistance force.
Distance Traveled by Forces
Effort force travels 4 times greater distance than
the resistance force.
Mechanical Advantage Ratios
One is the magic number
If MA is greater than 1:
• Proportionally less effort force is required to
overcome the resistance force
• Proportionally greater effort distance is required
to overcome the resistance force
If MA is less than 1:
• Proportionally greater effort force is required to
overcome the resistance force
• Proportionally less effort distance is required to
overcome the resistance force
MA can never be less than or equal to zero.
Ideal Mechanical Advantage (IMA)
• Theory-based calculation
• Friction loss is not taken into consideration
• Ratio of distance traveled by effort and
resistance force
• Used in efficiency and safety factor design
calculations
DE
DE
IMA =
D
R
= Distance traveled by effort force
DR = Distance traveled by resistance force
Actual Mechanical Advantage (AMA)
• Inquiry-based calculation
• Frictional losses are taken into
consideration
• Used in efficiency calculations
• Ratio of force magnitudes
FR
FR
AMA =
F
= Magnitude of resistance force
E
FE = Magnitude of effort force
Inclined Plane
A flat surface set at an angle or incline with
no moving parts
Able to lift objects by pushing or pulling the
load
Inclined Plane IMA
DE
IMA =
DR
DE = Distance traveled by the effort = L
DR = Distance traveled by the resistance = H
L(slope)
IMA =
H
What is the IMA of the inclined plane above?
IMA = 15.0 ft / 4.0 ft = 3.75 = 3.8:1
4.0 ft
Inclined Plane AMA
50 lb
FR
AMA =
FE
4 ft
What is the AMA of the inclined plane above?
50.lb
AMA =
20.lb
AMA = 2.5 = 2.5:1
What is the efficiency of the inclined plane above?
 AMA  100=  2.50 
100 = 67%
% Efficiency = 



 IMA 
 3.75 
Wedge
• Functions as a moving inclined plane
• Tapers to a thin edge and is used for splitting,
raising heavy bodies, or for tightening by being
driven into something
Wedge IMA
DE = Distance traveled by the effort = L
DR = Distance traveled by the resistance = H
L( to height)
IMA =
H
What is the IMA of the wedge shown?
IMA = 10.0 in. / 3.0 in. = 3.33 = 3.3:1
L 10.0 in.
DE
IMA =
DR
H 3.0 in.
250. lb
Wedge AMA
FR
AMA =
FE
700.lb
AMA =
250.lb
L 10.0 in.
What is the AMA of the wedge
shown?
H 3.0 in.
700. lb
700. lb
AMA = 2.80 = 2.80:1
What is the efficiency of the wedge
shown?
 AMA  100=  2.800 
100 = 84%
% Efficiency = 



 IMA 
 3.333 
Screw
Two Components
• An inclined plane wrapped
around a cylinder, forming
the path and pitch
• A wheel and axle used to
create rotary motion
Properties
• Change rotary motion into linear motion
• Used as a threaded fastener
• Large MA
• Large amount of friction loss
Screw Identification
Effort Arm Distance –
If using a wrench, effort arm
distance would be the length of
the wrench
Pitch
Thread Information
1/2 13 NC
Diameter
Thread
description
coarse or fine
Threads
per inch
Distance between threads
and linear distance traveled
by 1 rotation of the screw
Diameter
If 13 threads per inch, then pitch is 1/13 of an inch.
How far will a screw with 13 threads per inch move linearly if
turned one full rotation? 1/13 of a inch
Screw IMA
DE
IMA =
DR
1/4 20 NC
DE = One rotation of the effort arm = Circumference
DR = Linear distance traveled during one rotation
of the effort arm = Pitch
Circumference 2  π  r
IMA =
=
Pitch
P
What is the IMA of the screw above if effort is applied by an
8.0in. long wrench?
2  π  8.0in
IMA =
= 1005.31 = 1.0 •103
1in.
20
Screw AMA
1/4 20 NC
FR
AMA =
FE
35 lb
What is the AMA of the
screw shown?
1200lb
AMA =
AMA = 34.29 = 34:1
35lb
1200 lb
What is the efficiency of the screw shown?
 AMA  100=  34.29  100
% Efficiency = 
= 3.4%

 1005.3 
 IMA 


Why is efficiency so low?
Compound Machines
Simple machines working in combination to
complete a task
Calculating mechanical advantage
MATOTAL = MA1 MA2  MA3 ...
Image Resources
Microsoft, Inc. (2008). Clip art. Retrieved January 10, 2008,
from http://office.microsoft.com/en-us/clipart/default.aspx